Computer Aided Geometric Design - Special issue: Topics in CAGD
Geometric criteria on the higher order smoothness of composite surfaces
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Corner Blending of Free-Form N-Sided Holes
IEEE Computer Graphics and Applications
Best Fit Surface Curvature at Vertices of Topologically Irregular Curve Networks
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Fast and local fairing of B-spline curves and surfaces
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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The surfaces of complex free-form objects can typically be modeled by a hierarchy of primary surfaces, connecting surfaces and corner patches. Within the context of digital shape reconstruction, these surfaces simultaneously approximate measured data points, satisfy fairness criteria and adhere to continuity constraints according to their dependencies. A new framework algorithm is introduced to perfect existing B-spline surfaces; the algorithm alternates --- in a stepwise manner --- between continuity constraint satisfaction and fairing by the remaining degrees of freedom. Some well-known fairing methods are adapted to this framework. Constrained fairing for n-sided corner patches, composed of quadrilaterals, is also briefly discussed. A few examples illustrate the results.